Method for transient change detection with adaptive sampling, and detector implementing the method

ABSTRACT

A method of detecting transient changes in the distribution of a discrete time series includes: operating in a sparse mode wherein, at sniff periods successively repeated at a first rate, at most K test phases are performed, K being an integer superior or equal to two, each test phase consisting of analyzing, by a sampling stopping time determination unit, samples of the time series captured by a sampler at sampling times according to a second rate which is higher than the first rate to provide a positive or negative result of the test phase. If the results of K successive test phases of a sniff period are each positive, the method switches to operate in a dense mode wherein the sampler is operated to continuously capture samples of the time series at sampling times according to the second sampling rate.

TECHNICAL FIELD

The field of the invention is that of transient changes detection in thedistribution of a discrete time series. Such detection may findapplication in manufacturing (quality control), intrusion detection,spam filtering, website tracking, and medical diagnostics.

More particularly, the invention deals with detecting transient changesin a time series while operating with a limited sampling rate. Anillustrative example of the invention deals with data detection in anasynchronous communication.

STATE OF THE ART

Change point detection tries to identify times when the probabilitydistribution of a time series changes. Change-point detection problemsindeed consider a discrete time series which undergoes a local change indistribution from nominal distribution P0 to change distribution P1 atan unknown time. Before the change, the time series shows its nominaldistribution P0. From the time the change occurs, the time series isdistributed according to the change distribution P1. Then, after thechange of limited duration, the time series returns to its nominaldistribution P0.

Such detection problems have been investigated in a variety of studies.In [1], [2, Chap. 3], for instance, the CUSUM detection procedure,originally proposed to detect non-transient changes, is investigated fordetecting transient changes of given length. In [3, Section II.c], avariation of the CUSUM procedure is shown to achieve minimal detectiondelay in a certain asymptotic regime where the duration of the change istied to a (vanishing) false-alarm probability constraint. Finally, [4]proposed another CUSUM procedure that operates under a samplingconstraint and that is tailored for detecting non-transient changes.This procedure has the salient feature of skipping samples in the eventthat a change is unlikely to have occurred.

-   [1] B. Broder and S. Schwartz, “Quickest detection procedures and    transient signal detection,” DTIC Document, Tech. Rep., 1990.-   [2] C. Han, P. K. Willett, and D. A. Abraham, “Some methods to    evaluate the performance of page's test as used to detect transient    signals,” Signal Processing, IEEE Transactions on, vol. 47, no. 8,    pp. 2112-2127, 1999.-   [3] T. L. Lai, “Information bounds and quick detection of parameter    changes in stochastic systems,” Information Theory, IEEE    Transactions on, vol. 44, no. 7, pp. 2917-2929, 1998.-   [4] T. Banerjee and V. Veeravalli, “Data-efficient quickest change    detection in minimax settings,” Information Theory, IEEE    Transactions on, vol. 59, no. 10, pp. 6917-6931, October 2013.

DESCRIPTION OF THE INVENTION

The invention is focused on detecting a transient change in thedistribution of a sequential time series with a minimized detectiondelay subject to false alarm and sampling constraints. By a samplingconstraint, it is meant that an on-off observation control policy isimplemented, so as to sample the sequential time series only a fractionof time.

More particularly, the invention is directed at providing a method forrapidly detecting a transient change in a sequential time series via anadaptive sampling strategy minimizing the sampling rate while allowingto detect the change as efficiently as under full sampling.

To this purpose, the invention provides a transient change detectionmethod, wherein a sampler switches from operating in a sparse modewherein it captures samples during sniff periods successively repeatedat a first rate to operating in a dense mode wherein it captures samplesat a second rate which is higher than the first rate, the switching fromthe sparse mode to the dense mode being performed only if a series oftests performed on the samples captured during a sniff period arepositive and a sniff period being terminated as soon as a test of theseries of tests is negative.

A next test in the series of tests of a sniff period is performed onlyif the result of the previous test in the series of tests of the sniffperiod is positive, the next test phase being performed with analyzingat least as many samples as the previous test.

In an embodiment, the method of detecting transient changes in thedistribution of a discrete time series, comprises the steps of:

-   -   operating in the sparse mode wherein, at sniff periods        successively repeated at a first rate, at most K test phases are        performed, K being an integer superior or equal to two, each        test phase consisting of analyzing, by a sampling stopping time        determination unit, samples of the time series captured by a        sampler at sampling times according to a second rate which is        higher than the first rate to provide a positive or negative        result of the test phase;    -   if the results of K successive test phases of a sniff period are        each positive, switching to operate in the dense mode wherein        the sampler is operated to continuously capture samples of the        time series at sampling times according to the second sampling        rate; wherein a sniff period is ended as soon as the analyzing        of the at least one captured sample in a test phase of the sniff        period is negative, the sampling of the time series being        stopped until the next sniff period; and        wherein a next test phase of a sniff period is performed only if        the result of the previous test phase of the sniff period is        positive, the next test phase being performed with analyzing at        least as many samples as the previous test phase.

Preferred but non limitative features of this method are as follows:

-   -   a next test phase of a sniff period analyses exponentially more        samples that the previous test phase of the sniff period;    -   said analyzing the captured samples in a test phase by the        sampling stopping time determination unit comprises determining        a probability that said captured samples are typical of an        expected transient change in the distribution of a discrete time        series;    -   the transient changes correspond to information messages being        received at times which are unknown to a receiver which includes        said sampler and said sampling stopping time determination unit;    -   the absence of the expected transient change corresponds to        presence of noise only on an asynchronous data communication        channel by which the receiver receives the information messages;    -   it further comprises in the dense mode operating a decoder to        sequentially decode the samples captured at sampling times        according to the second rate.

The invention further extends to a transient change detector to detecttransient changes in the distribution of a discrete time series,comprising a sampler to capture samples of a time series and a samplingstopping time determination unit to control operation of the sampler andanalyze the captured samples, wherein the sampling stopping timedetermination unit is configured to switch operation of the sampler fromcapturing samples during sniff periods successively repeated at a firstrate to capturing samples at a second rate which is higher than thefirst rate, the sampling stopping time determination unit being furtherconfigured to perform switching of the sampler operation only if aseries of tests performed by the sampling stopping time determinationunit on the samples captured during a sniff period are each positive,and to terminate a sniff period as soon as a test of the series of testsis negative.

BRIEF DESCRIPTION OF THE DRAWINGS

Further characteristics and advantages of the invention will appear uponreading a preferential embodiment of the invention made in reference tothe appended figures in which:

FIG. 1 is a time representation of the method of the invention;

FIG. 2 is a flowchart illustrating the various steps of a possibleembodiment of the method of the invention;

FIG. 3 is a schematic diagram of a transient change detector accordingto a possible embodiment of the invention.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

The invention proposes a sequential time series change-point detectionmethod capable of detecting transient changes in a distribution. Thisprocedure has, at a high level, the following properties asymptotically:

-   -   1. it detects changes of minimal duration,    -   2. it detects changes with minimal delay,    -   3. it minimizes the sampling rate.

Property 1 means that no procedure can detect changes of smallerduration, irrespectively of their delay and sampling rate. Properties 2and 3 mean that among all procedures that detect changes of minimalduration, the proposed procedure simultaneously minimizes delay andsampling rate.

The invention relates to a method of identifying transient changes inthe activity of a time series. By transient change, it is meant atemporally bounded change that occurs randomly in a temporal series.Here the change, of fixed known duration n, from nominal distribution P0to change distribution P1, occurs at a random time v uniformlydistributed within a time frame of size A_(n)=2^(αn). A_(n) denotes theuncertainty level regarding the location of the transient change, and adenotes an uncertainty exponent.

With reference to FIG. 3, the method is implemented by a transientchange detector 1 which comprises a sampler 2 to capture samples of thetime series TS and a sampling stopping time determination unit 3 toanalyze the captured samples and control operation of the sampler.

The sampler 2 is sampling constrained by the sampling stopping timedetermination unit 3 and can observe only a fraction of the sequentialtime series. This sampling constraint is captured by a sampling rate ρ.

With ρ=1, the sampler 2 is always is always in the listening mode andsamples every points of the time series. In order for instance tominimize energy consumption of the sampler, and/or to minimize theamount of collected samples which may have to be stored and processed,it may be favorable to reduce the sampling rate so that the samplersamples only a fraction of the time series. With 0<ρ<1, ρ corresponds tothe ratio between the reduced sampling rate and the original samplingrate for observation of all points of the time series.

It has been demonstrated by the inventors that change detection can beperformed as efficiently as under full sampling with a reduced samplingrate and thus only a limited number of samples. More specifically, for afixed uncertainty exponent a E (0,D(P1∥P0)), the sampling rate p can bemade as small as ω(1/n) (in other words it dominates 1/n asymptotically)without any deterioration in asymptotic performance compared to fullsampling in terms of false alarm probability and detection delay. In theprevious sentence, D(P1∥P0) denotes the Kullback-Liebler divergencebetween the probability distributions P1 and P0. Conversely, ifα>D(P1∥P0) or if the sampling rate is o(1/n) (it is dominated by 1/nasymptotically), it is impossible to reliably detect the change.Accordingly, maximal performance can be reached, while sleeping (almost)all the time.

In order to capitalize upon these results, the present inventionproposes to implement an adaptive sampling strategy. In its most generalform, the adaptive sampling strategy consists of a family of algorithmsA_i, where the algorithm A_i makes a decision, that may be based on anysubset of previous sample(s), for example based on some form ofprobability threshold rule, to either sample position i or not.

According to an embodiment, it is sampled periodically roughly a small(constant) number of points, potentially a single point, of the timeseries out of every M points of the time series for a suitable value M.After each such set of sample(s), it is decided either to continuesampling if the recent sample(s) are (is) sufficiently unlikely to havebeen generated by the nominal distribution P0, or else to stop sampling.The decision to continue sampling becomes more stringent as more samplesare taken, thus limiting the average sampling rate.

An example embodiment of the invention consists of sampling based ontest phases. Each test phase has a length, and a probability thresholdsuch that it is moved from test phase i to test phase i+1 only if theprobability of the sample(s) observed in test phase i is sufficientlysmall under the nominal distribution. Note that there is a lot offlexibility in choosing the lengths and probability thresholds in thismulti-phase scheme to achieve asymptotically optimal performance. As aspecific example, it can be chosen to make the length of each test phaseexponential in the length of the previous phase, but it is emphasizedthat other choices, such as having the length grow by a constant factor,say double, in the initial phases still achieve the same asymptoticperformance. In general, the lengths and probability thresholds need tobe chosen so that the sampling rate is dominated by the first phase,which roughly translates to a condition of the formΣ_(i)p_(i)l_(i+1)=o(l₀(n)), where p_(i) is the probability (under thenominal distribution) of deciding to move from phase i to phase l_(i+1),is the number of samples taken in phase i+1, and l₀(n) is the number ofsamples taken in the first phase. Any such choice can be used to detectthe change-point with asymptotically optimal sampling rate.

It is emphasized that the test phases are not necessarily discretephases, but can be continuous as mentioned earlier, i.e. at each time i,an algorithm A_i can be used to decide whether to sample at time i basedfor instance on all previously taken samples. Hence, it is most generalform, the invention relates to a method of detecting transient changesin the distribution of a discrete time series, which comprises, at eachpoint in time, running a test to decide whether or not operating asampler to acquire a sample of the time series.

In one specific choice of lengths and probability thresholds, theinvention proposes to switch to higher sampling rates only if a seriesof tests have shown to be positive. The series of tests further allowsthe sampler to stop sampling in case the expected transient change isnot present.

To this respect, the invention proposes a transient change detectionmethod, wherein the sampler 2 switches from a sparse mode wherein itcaptures samples of the time series during sniff periods successivelyrepeated at a first rate f1 to a dense mode wherein it captures samplesof the time series at a second rate f2 which is higher than the firstrate (f1=k*f2, with 0<k<1). The second rate f2 is preferably set to 1 toensure full sampling of the time series when operating in the densemode.

The switching from the sparse mode to the dense mode is performed onlyif a series of tests performed on the samples captured during a sniffperiod are positive and a sniff period being terminated as soon as atest of the series of tests is negative.

According to a possible embodiment, in a sniff period of the sparsemode, the transient change detector 1 performs at most K test phases, Kbeing an integer superior or equal to two. Each test phase consists ofanalyzing, by the sampling stopping time determination unit 3, at leastone sample of the time series captured by the sampler 2 at samplingtime(s) according to the second rate f2 to provide a positive ornegative result of the test phase. Each test phase therefore implementsa binary hypothesis test for discriminating hypothesis H0 correspondingto nominal observations, against hypothesis H1 corresponding to changeobservations.

The sniff period is ended as soon as the analyzing of the capturedsample(s) in a test phase of the sniff period provide a negative result,the sampling of the time series being stopped until the next sniffperiod.

A next test phase of the sniff period is performed only if the result ofthe previous test phase of the sniff period is positive, the next testphase being performed with analyzing at least as many sample(s) as theprevious test phase. Preferably a next test is performed with analyzingmore samples than the previous test phase.

If the results of the K successive test phases of the sniff period areeach positive, the sampler 2 switches to operating in the dense mode.The dense mode lasts for at most n samples captured at the secondsampling rate f2. The sampler 2 therefore switches back to the sparsemode from the dense mode after having captured samples at the secondsampling rate f2 at most n successive times.

In an embodiment, in a test phase of a sniff period exponentially moresamples are analyzed than in the previous test phase of the sniffperiod.

In a sniff period, the analysis performed by the stopping timedetermination unit 3 may be identical or different from one test phaseto another. More than one analysis may be performed in a test phase, sothat the test phase is decided as positive or negative considering theresults of these various analyses.

Analyzing the captured samples in a test phase may comprise determininga probability that said captured samples are typical of an expectedtransient change. Said analyzing may comprise determining a probabilityof observing the analyzed captured samples in the presence, orrespectively absence, of the expected transient change, comparing theprobability to a threshold, and providing a positive result of the testphase if said probability is upper, respectively lower, than thethreshold.

Said analyzing the captured samples in a test phase may comprisecalculating the empirical distribution of the analyzed captured samplesand comparing said empirical distribution to a theoretical distributioncorresponding to the absence, or respectively presence, of the expectedtransient change.

A preferred although non limitative embodiment is now described withreference to FIG. 1 which shows a time representation of the method ofthe invention given for illustrative purpose.

The method starts in the sparse mode, with the sampler 2 taking samplesduring sniff periods SP1-SP6 successively repeated at the first rate f1,and which each starts at times Sj=┌j/(k*f2)┐, j being an integer.

At each Sj, the sampler 2 starts taking consecutive samples at thesecond rate f2. The stopping time determination unit 3 performs a firsttest T1 by analyzing a first set of consecutive samples. On FIG. 1, forpurely illustrative purpose, this first set comprises two consecutivesamples.

The first test T1 is negative at sniff periods SP1, SP2, SP5, SP6, sothat the sniff period is ended by the stopping time determination unit 3and sampling is not resumed before the next sniff period SP2, SP3, SP6.

As the first set T1 is positive at sniff periods SP3 and SP4, thestopping time determination unit 3 performs a second test T2 byanalyzing a second set of consecutive samples, larger than the firstset. On FIG. 1, for purely illustrative purpose, this first setcomprises the four consecutive samples after those used in the firsttest T1. Anyhow, in a more general manner, a next test phase may usetotally different samples than those of the previous test(s) (such asthe directly successive samples), or may use part or all of the samplesof the previous test(s).

The second test T2 is negative at sniff period S3, so that the sniffperiod is ended and sampling is not resumed before the next sniff periodSP4.

The second test T2 is positive at sniff period S3, so that a third testT3 is performed, here with eight consecutive samples. The third test T3is positive meaning that all the consecutive tests that can associatedwith a sniff period are positive, and the sampler 2 then switches todense mode taking samples continuously at the second rate f2.

When in the dense mode, the sampler takes samples continuously at saidsecond rate f2 for at most n steps. When switching back to the sparsemode, samples captured in the dense mode may be ignored or not in makingthe decision to sample densely or not in the future. In other words,only samples captured in the sparse mode may be or not analyzed todecide whether or not to switch to the dense mode.

FIG. 2 is a flowchart of the method according to a possible embodimentof the invention. The method starts in the sparse mode. At step 10, asniff period is started, while the number i of test phases isinitialized to one and the number p of samples to be captured by a testphase is initialized to log^((K))n, where log^((K)) denotes K iterationsof the log function:: log(log( . . . (log(n))). A test phase is thenperformed which consists at step 20 to capture p samples, at step 30 toanalyze the p captured samples, and at step 40 to verify whether or notthe test is positive. If the test if positive (low probability that thesamples are typical with the nominal distribution), it is checked atstep 50 whether all the K tests have been performed or not. If not, atstep 60, the number p of samples to be captured by the next test phaseis set to log^((K-i))n, and then the number of test phases i isincreased by one. The steps 20, 30, 40 are then reiterated.

If a test is negative (the samples are evaluated as typical with thenominal distribution) at step 40, then step 70 is performed whichconsists in ending the sniff period, stopping sampling and waiting untilthe next sniff period starts (step 10).

If it appears at step 50 that K positive tests have been performed, thenstep 80 is performed which consists in switching to the dense mode forcapturing at most n samples at the second rate f2.

The invention is not limited to the above-described method, but alsoextends as shown on FIG. 3 to a transient change detector 1 comprising asampler 2 to capture samples of a time series TS and a sampling stoppingtime determination unit 3 to control operation of the sampler andanalyze the captured samples, wherein the sampling stopping timedetermination unit 2 is configured to switch operation of the sampler 3from capturing samples during sniff periods successively repeated at afirst rate to capturing samples at a second rate which is higher thanthe first rate, the sampling stopping time determination unit beingfurther configured to perform switching of the sampler operation only ifa series of tests performed by the sampling stopping time determinationunit on the samples captured during a sniff period are each positive,and to terminate a sniff period as soon as a test of the series of testsis negative. The transient change detector 1 may further comprise astorage unit 4 where the samples corresponding to the transient changeand captured when the sampler 2 is operating in the dense mode can bestored and from which they can be retrieved.

An exemplary, although non limitative, example of application of theinvention relates to asynchronous data communication over a datacommunication channel between a transmitter and the receiver, thereceiver including the previously described transient change detector 1.In such an example, the transient change to be identified correspond toan information message being sent on the data communication channel at atime which is unknown to the receiver.

In this asynchronous data communication framework, the nominaldistribution of the observed time series corresponds to pure noise, thechange duration correspond to the lengths of the codewords sent on thedata communication channel and the change distribution corresponds tothe set of channel output distributions induced by the codewords.

Before and after the change, the receiver sees, at those times where itchooses to sample the channel output, independent and identicallydistributed noise. During the change, the receiver sees, at those timeswhere it chooses to sample the output, symbols c_(i)(m) of the codewordassigned to an information message.

The noise and the change distributions can be unified by modeling thetime series as carried over a data communication channel characterizedby its finite input and output alphabets X∪{*} and Y, respectively, andtransition probability matrix Q(y|x), for all yεY and xεX∪{*}. Thespecial symbol * denotes noise.

The receiver observes independent channel outputs Y₁, Y₂, . . . ,Y_(A+n-1) distributed as follows, depending upon time v at which thecodeword starts being sent:

-   -   for 1≦i≦v−1 or v+n≦i, the Y_(i)'s are “pure noise” symbols,        i.e., Y_(i)˜Q(•|*);    -   for v≦i≦v+n−1, Y_(i)˜Q(•|c_(i−v+1)(m)), where c_(i)(m) denotes        the i^(th) symbol of a codeword (m).

The codeword c(m) may start by a preamble P which size is greater thatthe sniff period repetition distance 1/f1 corresponding to the firstrate. This ensures that at least one symbol from the preamble iscaptured by the sampler in the sparse mode. Of course, the preamble'ssize is preferably chosen so as to allow for sampling a large number ofpreamble's symbols.

The preamble may consist of successive repetitions of a symbol a, whichis preferably chosen so that Q(•|a) strongly differs from Q(•|*). Theinvention is not limited to such an embodiment, but extends to the useof a preamble consisting of different symbols, preferably of symbolsthat predominantly differ from the symbol * denoting noise. The varioustests T1-T3 may be similar or not, but each consists in verifyingwhether the samples captured in a test are typical with Q(•|a).

In an embodiment, the preamble is made of s_(q)(n) symbols, with q aninteger superior or equal to one. The number of symbols s_(q)(n) may beequal to n/log^((q))n, where log^((g)) denotes q iterations of the logfunction:: log(log( . . . (log(n))).

Dealing with asynchronous data communication, not only change detectioncan be performed but also change isolation as decoding of thetransmitted data is performed at the receiver. Decoding happens based ona sampling strategy, a stopping rule defined on the sampled process, andan isolation rule which maps the stopped sampling process with apossible message. Here the sampling strategy and the stopping rule arethe ones described above.

As for the isolation rule, the receiver may perform sequential decodingimplemented at each step of the at most n steps if the dense mode basedon the past samples. If no codeword is decoded at the end of the n stepsof the sequential decoding operation, or as soon as a codeword isdecoded by the sequential decoding operation, the sampler switches fromoperating in the dense mode to operating in the sparse mode.

As a purely illustrative example, the sequential decoding is forinstance a sequential typicality decoding, whereby at a step of thedense mode, the empirical distributions induced by the last samples iscalculated. This empirical distribution is compared to the theoreticaldistribution induced by each codeword, and if there exists a message mfor which the distance in between the empirical distribution and thetheoretical distribution induced by the codeword assigned to the messageis lower than a threshold, then the receiver declares that message m wassent.

As an alternative, decoding may not be performed sequentially but onlyonce after n samples have been captured using a low complexity decoderfor any state-of-the-art channel code, e.g., an LDPC code or a turbocode. Once the dense mode is entered, the low-complexity decoder runs onthe n samples. If a codeword is found, the probability of the n observedsampled assuming that this codeword was sent is evaluated, and if thisprobability exceeds a threshold, decoding is stopped and this codewordis declared. If the probability does not exceed the threshold, or if nocodeword is found, e.g., the decoder fails to converge, the samplerswitches from operating in the dense mode to operating in the sparsemode.

What is claimed is:
 1. A method of detecting transient changes in thedistribution of a discrete time series, wherein a sampler switches fromoperating in a sparse mode wherein it captures samples of the timeseries during sniff periods successively repeated at a first rate tooperating in a dense mode wherein it captures samples of the time seriesat a second rate which is higher than the first rate, the switching fromthe sparse mode to the dense mode being performed only if a series oftests performed on the samples captured during a sniff period arepositive and a sniff period being terminated as soon as a test of theseries of tests is negative.
 2. The method of claim 1, comprising thesteps of: operating in the sparse mode wherein, at sniff periodssuccessively repeated at the first rate, at most K test phases areperformed, K being an integer superior or equal to two, each test phaseconsisting of analyzing, by a sampling stopping time determination unit,at least one sample of the time series captured by the sampler atsampling times according to the second rate which is higher than thefirst rate to provide a positive or negative result of the test phase;if the results of K successive test phases of a sniff period are eachpositive, switching to operate in the dense mode wherein the sampler isoperated to continuously capture samples of the time series at samplingtimes according to the second sampling rate; wherein a sniff period isended as soon as the analyzing of the at least one captured sample in atest phase of the sniff period is negative, the sampling of the timeseries being stopped until the next sniff period; and wherein a nexttest phase of a sniff period is performed only if the result of theprevious test phase of the sniff period is positive, the next test phasebeing performed with analyzing at least as many samples as the previoustest phase.
 3. The method of claim 2, wherein a next test phase of asniff period analyses exponentially more samples that the previous testphase of the sniff period.
 4. The method of claim 2, wherein saidanalyzing the captured samples in a test phase by the sampling stoppingtime determination unit comprises determining a probability that saidcaptured samples are typical of an expected transient change in thedistribution of a discrete time series
 5. The method of claim 4, whereinsaid analyzing the captured samples in a test phase comprisesdetermining a probability of observing the analyzed captured samples inthe presence, respectively absence, of the expected transient change,comparing the probability to a threshold, and providing a positiveresult of the test phase if said probability is upper, respectivelylower, than the threshold.
 6. The method of claim 5, wherein saidanalyzing the captured samples in a test phase comprises calculating theempirical distribution of the analyzed captured samples and comparingsaid empirical distribution to a theoretical distribution in thepresence, respectively absence, of the expected transient change on thedata communication channel.
 7. The method of claim 1, wherein thetransient changes correspond to information messages being received attimes which are unknown to a receiver which includes said sampler andsaid sampling stopping time determination unit.
 8. The method of claim7, wherein the absence of the expected transient change corresponds topresence of noise only on an asynchronous data communication channel bywhich the receiver receives the information messages.
 9. The method ofclaim 7, wherein a transient change in the distribution is a changesequence which comprises a preamble which size is larger than the periodcorresponding to the first rate separating two successive sniff periods.10. The method of claim 9, wherein the preamble consists of successiverepetitions of a symbol.
 11. The method of claim 10, wherein the changesequence is made of n successive symbols consisting of n/log^((q))nsymbols for the preamble and n−n/log^((q)) n symbols for a codeword,where log^((q)) denotes q iterations of the log function.
 12. The methodof claim 11, wherein a test of a sniff period analyses log^((K-i))nsamples and a next test of the sniff period analyses log^((K-(i+1))n,with i an integer comprises between 0 and K−2.
 13. The method of claim9, wherein the number of samples captured in the dense mode is at mostthe number of symbols that compose the change sequence.
 14. The methodof claim 13, further comprising in the dense mode operating a decoder tosequentially decode the samples captured at sampling times according tothe second rate.
 15. The method of claim 14, further comprising, if nocodeword is decoded at the end of the sequential decoding operation, oras soon as a codeword is decoded by the sequential decoding operation,switching from operating in the dense mode to operating in the sparsemode.
 16. A transient change detector comprising a sampler to capturesamples of a time series and a sampling stopping time determination unitto control operation of the sampler and analyze the captured samples,wherein the sampling stopping time determination unit is configured toswitch operation of the sampler from capturing samples during sniffperiods successively repeated at a first rate to capturing samples at asecond rate which is higher than the first rate, the sampling stoppingtime determination unit being further configured to perform switching ofthe sampler operation only if a series of tests performed by thesampling stopping time determination unit on the samples captured duringa sniff period are each positive, and to terminate a sniff period assoon as a test of the series of tests is negative.